Question

Can someone please help me I'm very stuck geometry isn't my thing ​

Answer 1

1. (10, -⁸/₃)

2. (2, ⁸/₃)

3. (12, -4)

Explanation:

I will do the first 3 as examples.

1. Y is ⅔ of the distance from X to Z.

Y − X = ⅔ (Z − X)

The x-coordinate of Y is:

x − -6 = ⅔ (18 − -6)

x + 6 = ⅔ (24)

x + 6 = 16

x = 10

The y-coordinate of Y is:

y − 8 = ⅔ (-8 − 8)

y − 8 = ⅔ (-16)

y − 8 = -³²/₃

y = -⁸/₃

Y is at (10, -⁸/₃).

2. The ratio of XY to YZ is 1:2.

(Y − X) / (Z − Y) = 1 / 2

Cross multiply.

2 (Y − X) = Z − Y

The x-coordinate of Y is:

2 (x − -6) = 18 − x

2x + 12 = 18 − x

3x = 6

x = 2

The y-coordinate of Y is:

2 (y − 8) = -8 − y

2y − 16 = -8 − y

3y = 8

y = ⁸/₃

Y is at (2, ⁸/₃).

3. Y is ¼ of the distance from Z to X.

Y − Z = ¼ (X − Z)

The x-coordinate of Y is:

x − 18 = ¼ (-6 − 18)

x − 18 = ¼ (-24)

x − 18 = -6

x = 12

The y-coordinate of Y is:

y − -8 = ¼ (8 − -8)

y + 8 = ¼ (16)

y + 8 = 4

y = -4

Y is at (12, -4).